This paper describes a statistical framework for object alignment by pose clustering. The idea underlying pose clustering is to transform the alignment process from the image domain to that of the appropriate transformation parameters. It commence by taking k-tuples from the primitive-sets for the model and the data. The size of the k-tuples is such that there are sufficient measurements available to estimate the full-set of transformation parameters. By pairing each k-tuple in the model and each k-tuple in the data, a set of transformation parameter estimates or alignment votes is accumulated. The work reported here draws on three ideas. Firstly, we estimate maximum likelihood alignment parameters by using the the EM algorithm to fit a mixture model to the set of transformation parameter votes. Secondly, we control the order of the underlying mixture model using a minimum description length criterion. Finally, we limit problems of combinatorial background by imposing structural constraints on the k-tuples.